Seminar Analysis: Luca Martinazzi (Rutgers)
We study the Moser-Trudinger equation Δu = λu Exp(u2), λ>0 on a 2-dimensional disk, arising from the Moser-Trudinger sharp embedding of H10(Disk) into the Orlicz space of functions u with Exp(u2) integrable. We answer some long standing open questions:
a) The weak limit of a blowing-up sequence of solutions to the Moser-Trudinger equation on a disk is 0.
b) The Dirichlet energy of a blowing-up sequence of solutions on a disk converges to 4π.
c) For L large enough, the Moser-Trudinger equation on a disk admits no solution with Dirichlet energy larger than L.
This work is joint project with Andrea Malchiodi (SISSA - Trieste).
Export event as
iCal